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Write all trigonometric ratios of angle …

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Write all trigonometric ratios of angle A in terms of sec A
  • 1 answers

Yogita Ingle 4 years, 6 months ago

We know that,
sec A = 1/cos A
⇒ cos A = 1/sec A
cos²A + sin²A = 1
⇒  sin²A = 1 – cos²A
⇒  sin²A = 1 – (1/sec²A)                          (cosA= 1/secA)
⇒  sin²A = (sec²A-1)/sec²A

⇒sinA = √((sec²A-1)/sec²A)

sinA = √(sec²A-1) ÷ (secA)............................(i)

sin A = 1/cosec A
⇒ cosec A = 1/sin A

cosecA= secA ÷√sec²A-1                 (from eq i)
Now,
sec²A – tan²A = 1
⇒ tan²A = sec²A + 1

tanA = √sec²A + 1.....................................(ii)

tan A = 1/cot A
⇒ cot A = 1/tan A

cotA  = 1/√sec²A + 1                  (from eq ii)

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